Suppose that a particular candidate for public office is favored by 48% of all registered voters in the district. A polling organization will take a random sample of 500 of these voters and will use ˆp, the sample proportion, to estimate p.
a. Show that sˆ , the standard deviation of ˆ p , is equal to 0.0223.
b. If for a different sample size, s ˆ = 0.0500, would you expect more or less sample- to- sample variability in the sample proportions than when n = 500?
c. Is the sample size that resulted in sˆ p = 0.0500 larger than 500 or smaller than 500? Explain your reasoning.